Paper is commonly formed by injecting stock through a headbox onto a moving fourdrinier forming wire screen which moves at approximately the same speed as the flow of stock being ejected from the headbox. In some circumstances the stock is injected between two moving wire screens on a so-called twin wire machine. The stock is a mixture that usually contains one-half to one percent paper fibers and at least ninety-nine percent water. The water is drawn from the stock through the forming screens or wires, leaving a web of paper fibers which is pressed and dried to form a web of paper.
The stock is pumped into the headbox and ejected through a slice lip at an extremely high pressure by means of pumping equipment. An attenuator is disposed upstream relative to the headbox for damping pressure pulses caused by the stock pumping equipment. The arrangement is such that the rate of stock entering the headbox is relatively constant.
Modern papermaking machines are between one hundred and four hundred inches wide and operate at speeds up to and in excess of 4,000 feet per minute. Thus, the headbox and the slice that supply the flow of paper stock which is formed into the paper web must supply not only a large quantity of stock to meet the high forming speeds of modern papermaking processes, but must also supply the stock in an extremely uniform fashion if the sheet of paper formed is to be of uniform thickness across the width of the web, and to have uniform properties throughout.
Typically the stock is injected in a cross-machine direction through an inlet to a tapered inlet header. The inlet header has an array of tube inlets along one side corresponding to a plurality of tubes vertically arrayed in a tube bank through which the stock is diverted towards a nozzle terminating in a slice lip. The tube bank is typically in the neighborhood of six tubes high by several hundred tubes long. Accordingly, it is essential that the rate of flow of stock at the inlet of a tube positioned at one end of the inlet header be the same as the rate of flow of stock at the inlet of a tube positioned at the other end of the inlet header. If the stock has been thoroughly mixed and is of uniform consistency, and if the slice lip opening is the same along the entire cross-machine directional width of the headbox, the weight of the fibers within the stock per inch of width across the ribbon of stock ejected through the slice lip should be constant. The resulting web will have the desired uniform basis weight in the cross-machine direction.
In order to achieve the constant flow rate at the tube inlets located along one side of the inlet header, the inlet header is tapered in the cross-machine direction. In other words, the width of the inlet header decreases moving from the inlet end in the cross-machine direction towards the outlet or recirculation end. In a conventional header, the rate of change in cross-sectional area of the inlet header moving from the inlet end to the recirculation end is constant. This is illustrated by a straight-line relationship in a graph of the change in cross-sectional area versus distance along the inlet header. As a result of the tapered construction, the cross-sectional area of the inlet header moving in the cross-machine direction from the inlet end towards the recirculation end is reduced by an area substantially equal to three times the total cross-sectional area of the individual tube inlets not yet reached upstream of the cross-sectional area of the inlet header. This reduction in cross-sectional area of the inlet header compensates for the pressure lost as a result of the diverted flow of stock through the inlet tubes, thereby maintaining the same pressure at each inlet tube in the inlet header. Consequently, the rate of flow of stock through all the inlet tubes in a cross-machine direction is maintained substantially constant and equal.
In practice, care must be taken to prevent variation in paper weight or thickness in the cross-machine direction. In an effort to maintain a uniform paper weight across the paper web, some paper forming headboxes use actuators placed on the lip of the slice to deform the slice lip, thereby changing the width of the slice opening. In one recently developed system, described in U.S. Pat. No. 5,196,091 to Richard E. Hergert and incorporated herein by reference, the injection of diluting water into the headbox inlet header or manifold adjacent to the tube inlets has been used to control the dilution of the stock in the cross-machine direction. This dilution control in turn acts to control the paper web weight or thickness. This technique has produced paper webs having more uniform characteristics.
In order to obtain the ideal pressure distribution across the tube bank, the change in cross-sectional area per unit width of the headbox will not be constant, but will ideally increase as the header approaches the recirculation end. This type of header is usually known as a parabolic header because a graph of the area versus distance along the header is parabolic rather than straight-lined in nature. One method used to construct a header having the ideal parabolic relation of cross-sectional area from the inlet end to the recirculation end using a straight-tapered inlet header is to construct the inlet header with at least one side curved in the cross-machine direction. Another is to use a series of straight-tapered sections with differing tapers. Both of these solutions are complicated and expensive to produce.
Because the ideal pressure distribution across the tube bank is achieved with a header having a parabolic increase in change in cross-sectional area as it approaches a recirculation end, there is a need to construct a parabolic header that is as easy and cost-efficient to produce as a single straight-tapered header.